Intermediate Moment Curve Calculator
Deflection at station x for a cantilever moment at a. x = a is the at-the-moment page. x = L is the free-end page. Runs locally.
Trust summary CVP VERIFIED · production STALE · CVP protocol 1.0.0-proposed · Engineering assurance
- Input interpretation
- Enter values to calculate.
- Result
- —
- Assurance
- Engineering
- Declared partition coverage
- PASS · 2/2 declared partitions (domain, invalid-domain) · Matrix
- Known limitations
- Physics L1 gap capability
- Core CVP does not include live graph, viewport, or pointer interaction.
- Model
- Deflection at a stated station for a cantilever moment at distance a from the wall.
- Scope
- Calculation runs locally in the browser; values are not uploaded.
- Verification
- Engine tested · Source checked · v1.0.0 · CVP VERIFIED · production STALE · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
- Versions
- Calculation 1.0.0 · CVP protocol 1.0.0-proposed
- CVP identity
- 0/0 property · digest c474a01cb827
- Legacy regression
- 3/3 tests · Production surface contract 6/6
- Trust layers
- Verification VERIFIED · Production STALE · overall VERIFIED_STALE
- CVP status
- STALE · Capability production binding: STALE · Site report: STALE · Evidence changed after the last successful production attestation. Re-attestation required.
- Reference
- O1 model · O2 expected_values · O2 numerical_behavior
- Interfaces
- PASS · UI (SSR) / REST / MCP
- Supplemental domain review
- Not performed
- Named expert review
- Not performed
- CVP suite
- 1/1 golden · 1/1 CVP boundary · 1/1 invalid · 1/1 cross-interface · 6/6 CVP contract · Manifest
- Sources
- Hibbeler, Mechanics of Materials
- Gere and Goodno, Mechanics of Materials
- Evidence
- 2 legacy golden · 1 legacy boundary · legacy regression suite · 1/1 oracle-backed golden · 1/1 invalid · Artifact integrity PASS
- Semantic contract
- PASS
Full verification
Formulas
Core equations used by this calculator.
How to use
Enter the moment, its position, the station, the length, the modulus, and the area moment
a and x must lie on the cantilever.
Read the deflection at x
Past the moment the slope is constant.
Example calculations
Common configurations with formula and result.
At the moment
M = 4, a = 1, x = 1, L = 2, E = 1, I = 1
At the free end
M = 4, a = 1, x = 2, L = 2, E = 1, I = 1
Intermediate Moment Curve calculator specification
Version 1.0.0 · Engine tested
- Engine tested 3/3 tests · Production surface contract 6/6
- Named expert review Not performed
- Calculation version 1.0.0
- Definition
- A cantilever of length L carries one moment M at distance a from the wall. For x ≤ a, δ = M x²/(2 E I). For x ≥ a, δ = M a (2x − a)/(2 E I).
- What it calculates
- Deflection at a stated station for a cantilever moment at distance a from the wall.
- Inputs
- M
- a
- x
- L
- E
- I
- Outputs
- delta
- Formula
Two-piece curve. x = a is the at-the-moment page. x = L is the free-end page.- Assumptions
- Calculation runs locally in the browser; values are not uploaded.
- Keep units consistent with the labels on each field.
- x = a recovers the at-the-moment page. x = L recovers the free-end page.
- Units
- M, a, x, L, E, and I set the deflection unit.
- Boundary conditions
- missing M, a, x, L, E, or I → MISSING_REQUIRED_INPUT
- L ≤ 0, E ≤ 0, or I ≤ 0 → VALUE_MUST_BE_POSITIVE
- a or x outside (0, L] → INVALID_INPUT
- Example
- M=4 a=1 x=2 L=2 E=1 I=1 → δ=6
- Validation cases
3 published on this page · 3/3 tests · Production surface contract 6/6 · View evidence
- M=4 a=1 x=1 L=2 E=1 I=1 → δ=2
- M=4 a=1 x=2 L=2 E=1 I=1 → δ=6
- a=3 L=2 → INVALID_INPUT
- Sources
- Hibbeler, Mechanics of Materials — Deflection of beams — cantilever with an intermediate momentSupports: x = a gives M a²/(2 E I) and x = L gives M a (2L − a)/(2 E I).
- Gere and Goodno, Mechanics of Materials — Deflection of beams — cantilever coupleSupports: Supports the straight tangent past the moment.
- Hibbeler, Mechanics of Materials — Deflection of beams — cantilever with an intermediate moment
- Calculation version
- 1.0.0
Background
Interpretation and common distinctions.
Find the deflection at a stated station for a cantilever moment at distance a from the wall.
Agent / API notes
Capability id: mechanical.statics.cantilever_moment_at_curve_deflection · tool id: cantilever-moment-at-curve · pin 1.0.0.
{ "M": 4, "a": 1, "x": 2, "L": 2, "E": 1, "I": 1 }
Related tools
Other calculators in this family: Angled Pull Calculator, Angled Pull on an Incline Calculator, Area Moment Calculator, Beam Deflection Calculator, Beam Moment Deflection Calculator, Beam Moment Maximum Deflection Calculator, Bending Stress Calculator, Cantilever Deflection Calculator . Explore all Statics & Strength.
Frequently asked questions
Key distinctions behind the calculation.
What is halfway to the moment?
For M = 4, a = 1, and x = 0.5 the deflection is 0.5.